According to Webster's (a work used far too often to make a point than it was ever intended to), a scar is, among other things, a "mark left on the skin or other tissue after a wound, burn, ulcer, pustule, lesion, etc. has healed," a "marring or disfiguring mark on anything", and "the lasting mental or emotional effects of suffering or anguish". Given these definitions, it becomes clear that the the scar is an apt analogy for the hypertext link.
The first definition of the scar defines it as a joining, that is, a visual signal that two pieces of skin that were not contiguous at one time now are. In this sense, a scar is the biological version of the seam, where Mother Nature (or, in the case of Frankenstein and Patchwork Girl, a human creator) sews flesh together in the same way a seamstress stitches together a quilt or the creator of a hypertext links texts together.
The second definition presents the scar as a mark of disfigurement. Scars are ugly (in modern Western society, at least). They're jarring breaks in the otherwise even epidermis (though, in the case of grafts, the skin on each side of the scar is of a different shade; Mary/Shelley/Jackson's creature's skin, composed entirely of grafts, is thus a visual patchwork). Similarly, the presence of the link is a disruption to the otherwise linear text. Its appearance is even similar; most graphical browsers will display a "scar" beneath the links on this page, though a user can play the role of cosmetic surgeon and opt to conceal this disfigurement of the text if they so choose.
The last of the Webster's definitions gives the scar a more abstract meaning; it is now a sign of trauma. In order for a scar to exist, the flesh must have been torn. The formation of a scar is a kludge: its appearance is the result of haphazard regeneration rather than orderly growth. The link is similarly a textual trauma; the transitions between sentences and paragraphs give way to (presumably) intuitive leaps between texts and ideas. The replacement (as opposed to the appending) of text caused by following an HTML link is disorienting to say the least; even the sudden appearance of another window (in an environment such as Storyspace) interferes with the reader's practiced down-and-to-the-right movement across a "page" of text.